Construction of warfarin population pharmacokinetics and pharmacodynamics model in Han population based on Bayesian method

The purpose of this paper is to study the genetic polymorphisms of related gene loci (CYP2C9*3, VKORC1-1639G > A) based on demographic and clinical factors, and use the maximum a posterior Bayesian method to construct a warfarin individualized dose prediction model in line with the Chinese Han population. Finally, the built model is compared and analyzed with the widely used models at home and abroad. In this study, a total of 5467 INR measurements are collected from 646 eligible subjects in our hospital, and the maximum a posterior Bayesian method is used to construct a warfarin dose prediction that conforms to the Chinese Han population on the basis of the Hamberg model. The model is verified and compared with foreign models. This study finds that body weight and concomitant use of amiodarone have a significant effect on the anticoagulant effect of warfarin. The model can provide an effective basis for individualized and rational dosing of warfarin in Han population more accurately. In the performance of comparison with different warfarin dose prediction models, the new model has the highest prediction accuracy, and the prediction percentage is as high as 72.56%. The dose predicted by the Huang model is the closest to the actual dose of warfarin. The population pharmacokinetics and pharmacodynamics model established in this study can better reflect the distribution characteristics of INR values after warfarin administration in the Han population, and performs better than the models reported in the literature.


Pharmacodynamic analysis of population pharmacokinetics
Hamberg's model is currently widely used for the individualized use of warfarin, This article will estimate model parameters applicable to Han Chinese populations based on this model (set as a reference literature model) 10 and based on extensive Chinese population data (646 subjects from 9 centers in different regions of China with 8352 drug records and 5467 INR measurements).The methodology for the construction and evaluation of the model is described in the supplementary material.

Data analysis
NONMEM (Version 7.4, ICON Development Solutions, USA) is used to establish population pharmacokinetic and pharmacodynamic model and model simulation; the plug-in of the running interface is Wings for NON-MEM; R software (Version 3.6.3) is used for drawing.In covariate screening, the covariates is firstly investigated and the model parameter EC50 values are analyzed by the graphical method, and the significantly correlated covariates were screened (P < 0.05).In addition to CYP2C9 genotype, VKORC1 genotype and age, this study will also examine factors that effect on model parameter EC50 values, such as body weight, body mass index, gender, concomitant use of amiodarone, azole antibiotics, statins and broad-spectrum antibiotics.Model evaluation uses the Bootstrap method to perform 1000 replaceable repeated sampling to obtain the median and 95% confidence interval of the model parameter distribution, and compare them with the model parameters obtained from the original data set, so as to evaluate the stability of the model parameters.

Ethical standards
All selected patients have signed the informed consent.This study has been approved by the hospital ethics committee (2016KY036, 2020KY006).

Basic clinical information
A total of 5467 INR measurements are collected from 646 subjects.The daily dose of warfarin ranges from 0.625 to 6.25 mg, and the frequency of administration is once a day.The time of INR measurement is distributed within 24 h after administration, mainly in 7-10 h after administration.
In this study, the data of subjects with ID of 1-114 (a total of 109 subjects with 969 INR measurements) are designated as the validation data set, and the data of subjects with ID of 115-1103 (a total of 537 subjects) are designated as validation data sets (in total of 537 subjects and 4498 INR measurements.The general characteristics of the subjects are detailed in Table 1.

Alfalfa-Warfarin-PPK/PD model and evaluation
The correlation analysis shows that the inter-individual variation value (ηEC 50 ) of the model parameter EC 50 is significantly correlated with body weight, body mass index and amiodarone (P < 0.05), while the correlation between other covariates and the model parameters is not significant (P > 0.05) (Fig. 1).It is manifested as a significant decrease in the EC 50 value when amiodarone is combined, that is, the effect value of anticoagulation increases under the same warfarin dose; When body weight or body mass index increases, the EC 50 value increases, that is, the anticoagulant effect value decreases at the same warfarin dose.
The graphical correlation analysis shows that the inter-individual variation value of model parameter EC50 (ηEC50) has a more significant correlation with body weight, and it is easier to consider the clinical use of body weight.Therefore, this study finally selects body weight to be included in the covariate analysis (Table 2).
In addition to the covariates included in the base model, the newly added covariate model of the reconstructed model is expressed as follows: EC50 = TVEC50 × (WT/60)1.34-CM1× 0.602.
In the formula, WT is body weight, CM1 is whether amiodarone is used in combination, 1 represents combined use, and 0 represents no combination.The TVEC50 value is a typical value of the EC50 value, and the TVEC50 value of different VKORC1 genotypes is different.For details, please refer to the methodological covariate model construction section.The model results show that when amiodarone is used in combination, the EC50 value of the anticoagulant effect will decrease by 0.602 mg/L, and the EC50 value of the anticoagulant effect will increase by 22.9% for every 10 kg increase in body weight.1000 times Bootstrap repeated sampling method is used for internal verification, of which 845 times parameters are successfully estimated, and the results are analyzed.The results show (Table 3) that the 95% confidence interval of the newly added covariate parameters in the Alfalfa-Warfarin-PPK/PD model does not include 0, indicating that the newly added covariates have a significant impact on EC50 and are not affected by the sample, so the Alfalfa-Warfarin-PPK/PD model retains the above covariates.In addition, the median parameter estimation obtained by Bootstrap is basically consistent with the parameter estimation value of the original data set, which reflects the stability of the model parameter estimation.
The goodness-of-fit graph (Supplementary Material Figs. 2 and 3) shows that, compared with the basic model, the Alfalfa-Warfarin-PPK/PD model has a certain degree of improvement in the goodness-of-fit to the data, and the outliers of CWRES are slightly reduced compared to the basic model.

External Verification of Alfalfa-Warfarin-PPK/PD Model
The model parameters in the established Alfalfa-Warfarin-PPK/PD model and the literature model 11 are fixed, and the INR in the validation dataset is predicted and compared with the measured value to evaluate the extrapolation performance of the two models.
The results show that both reconstructed Alfalfa-Warfarin-PPK/PD model and the literature model have good predictive ability for the INR data in the validation dataset, and the predicted value is very close to the measured value distribution (Supplementary Material Fig. 4).The OFV calculated by the literature model for the verification data set is 15.288, while the OFV calculated by the Alfalfa-Warfarin-PPK/PD model for the verification data set is − 238.464, which is far lower than the former, indicating that the prediction of the Alfalfa-Warfarin-PPK/ PD model is better on INR in the validation dataset.In addition, it can be seen from the model diagnostic diagrams (Supplementary Material Figs. 5 and 6) that the CWRES outliers (> 6) under the Alfalfa-Warfarin-PPK/ PD model are significantly less than the literature model, which also suggests that the Alfalfa-Warfarin-PPK/ PD model performance is better.(SEX: Sex, 1 for male, 2 for female; CM1: whether amiodarone, 0 unsuitable, 1 combined; CM2: azole antibiotics, 0 useless, 1 combined; CM3, statin, 0 useless, 1 combined; CM4: broad spectrum antimicrobial, 0 unsuitable, 1 combined; AGE: Age; WT: body weight; BMI: Body mass index).

Comparison of Alfalfa-Warfarin-PPK/PD model and other multiple prediction models
At present, there are many warfarin dose prediction models established based on gene polymorphisms, which can better improve the accuracy of individualized warfarin medication.However, there are not many evaluations of its efficacy, especially less evaluation of the predicted efficacy of different stable dose components.The reconstructed warfarin dose prediction model is verified and evaluated, and its performance is compared with various prediction models recognized at home and abroad, so as to evaluate which models have better performance and are more suitable for Han population.A representative model is selected based on the number of people, race, relevant inclusion factors, and whether prospective validation performed in the dose prediction models.These prediction models are used to predict the stable dose of warfarin for the whole group of patients, and the prediction percentage and the mean of absolute mean of error (MPE) are used to evaluate the efficacy of the warfarin dose prediction model.

Comparison of the prediction dose of warfarin between the Alfalfa-Warfarin-PPK/PD model and other models
The warfarin dose is calculated by the warfarin model formula, and the prediction dose and the actual dose of warfarin are plotted as a scatter plot to obtain the Pearson coefficient.The results show that there is a correlation between prediction dose and actual dose in each model (P < 0.001), and they are evenly distributed on both sides of the regression line.See Fig. 2 and Supplementary Material Table 2.

Results of the mean absolute error of each model
In this part of the study, the models with MPE values less than the minimum divided dose of warfarin of 0.625 mg 12 includes the Alfalfa-Warfarin-PPK/PD model and the Hamberg model, which are 0.390 mg/day and 0.427 mg/day, as shown in Supplementary Material Table 3. www.nature.com/scientificreports/

Results of prediction percentage of each model
The model with the highest ideal prediction percentage is the Alfalfa-Warfarin-PPK/PD model, followed by the Hamberg model.These two models are 72.60% and 51.15% respectively, as shown in Supplementary Material Table 4.

Discussion
This

Effect of CYP2C9 gene polymorphism on warfarin PK
The studies by Ma et al. confirm that CYP2C9 gene polymorphism can explain approximately 5-10% of the interindividual warfarin variation 13 ; the studies by Hamberg et al. show that the clearance difference between different CYP2C9 genotypes is as high as 4.2-fold 14 .Several studies show that CYP2C9 gene polymorphisms can affect the pharmacokinetic parameters of warfarin, and they are included in the model parameters when constructing a warfarin PK/PD model [13][14][15] .Several studies show that the CYP2C9 gene polymorphism significantly affects the clearance rate of warfarin, and the *2 or *3 genotype are the main genetic risk factor for excessive anticoagulation and bleeding events of warfarin [16][17][18] .The results of this study shows that the CYP2C9 *1/*1 genotype has the highest clearance rate of warfarin, followed by *1/*2, *1/*3, *2/*2, *2or*3, CYP2C9 *3/ *3 Genotype has the lowest clearance rate of warfarin.Incorporating the CYP2C9 genotype into the model parameters will more accurately predict the dose of warfarin, avoid excessive anticoagulation, and reduce the occurrence of bleeding events.

The effect of VKORC1 gene polymorphism on warfarin PD
The studies by Ma et al. confirm that VKORC1 gene polymorphism can explain about 20-25% of the interindividual warfarin variation 14 , and the studies by Hamberg et al. 11 show that it's up to twofold difference in EC50 between different VKORC1 genotypes.Several studies also show that VKORC1 genotype polymorphism can affect the pharmacodynamics of warfarin, and it is included as a model parameter in the construction of warfarin PPK/PD models [14][15][16] .Several studies show that the VKORC1-1639 genotype polymorphism affects the anticoagulant effect of warfarin, and is significantly associated with excessive anticoagulation and bleeding events in the primary phase of warfarin use 14,18,19 .This article shows that the VKORC1-1639 genotype polymorphism has a strong correlation with the model parameter EC50 value (P < 0.05), among which the VKORC1-1639GG genotype has the highest EC50 value (9.30 mL/min), VKORC1-1639GA genotype is the second (5.64 mL/min), and VKORC1-1639AA is the smallest (1.98 mL/min).Therefore, VKORC1-1639 is included in the model parameters.
For patients with genetic variation, if they can understand their genetic information before or in the early stage of medication, predicting the dose according to the model formula can not only help clinicians or pharmacists understand the dose required by patients as soon as possible, but also shorten the time to reach the target INR, which can also reduce the number of repeated blood draws, reduce costs, and increase patient compliance.

The effect of age on warfarin PK
Several studies show that although the protein binding capacity of warfarin does not change with age, its clearance rate in the body decreases with age, and the efficacy of warfarin gradually increases [20][21][22][23][24][25][26] .The studies of Vear et al. show that genetic polymorphisms affect the pharmacokinetics and pharmacodynamics of warfarin, and the effect of genetic polymorphisms increases with age 27 .In this study, age is introduced into the model parameter CL, and the results show that the value of CL decreased by 0.571% for every 1-year increase in age.Therefore, when using warfarin clinically, the effect of age on the stable dose of warfarin should also be considered.

Effects of body weight and gender on warfarin PD
Relevant studies show that when patients with BMI ≥ 40 kg/m 2 (or body weight > 120 kg) and body weight < 50 kg use oral anticoagulants, drug distribution and metabolism will be significantly affected 28,29 .Studies by Lane 26 and Xu 30 also show that patient weight can significantly affect S-warfarin clearance, affect the pharmacokinetics of warfarin, and thus affect pharmacodynamics.This study shows that when body weight or body mass index increases, the EC50 value increases.That is, under the same warfarin dose, the effect value of anticoagulation decreases.When the body weight increases by 10 kg, the EC50 value will increase by 22.9%.This part of the study analyzes the correlation between gender and model parameter EC50 value.The P > 0.05, which indicates that gender difference has no significant effect on the PD of warfarin.The studies by Hamberg and Lin Rongfang et al. also show that age has no significant effect on the model parameter EC50 in the study of warfarin PK/PD model, and has not been included in the model construction.

Effect of concomitant medication on warfarin PD
For warfarin combined with amiodarone, several studies demonstrate that amiodarone has a significant effect on the anticoagulant effect of warfarin 31,32 .In this study, it shows that when patients are combined with amiodarone, the EC50 value of the anticoagulant effect will decrease by 0.602 mg/L.So to achieve the same anticoagulant effect, patients combined with amiodarone must reduce the dose of warfarin.
For the relationship between azole antifungals and warfarin PD, related studies prove that azole antifungals are substrates and inhibitors of cytochrome P450 isoenzymes 33 , and the metabolism of warfarin needs to pass through P450 enzymes.So when warfarin is combined with azole antifungals, the anticoagulant effect of warfarin is enhanced to some extent.The results of this study show that azole antifungal drugs have no effect on the EC50 of warfarin.On the one hand, it may be that the patients included in this study have fewer azole antifungal drugs.On the other hand, more than 50% of the patients taking azole antifungal drugs may have used itraconazole, which has no inhibitory effect on CYP2C9.Most of the remaining patients use fluconazole and voriconazole with weaker inhibitory effects, so the overall sample has a small impact on the anticoagulant effect of warfarin.
For the association of statins with warfarin PD, a number of studies show that fluvastatin can significantly increase the anticoagulation intensity of warfarin, atorvastatin does not affect the anticoagulation intensity of warfarin, and there are large individual differences in the effect of rosuvastatin on the anticoagulation intensity of warfarin.In this study, the model parameter EC50 of statins and warfarin show little correlation, which may be because the patients included in this study who take atorvastatin without affecting anticoagulation intensity accounted for more than 70% of the total patients taking statins.The overall sample has no effect on the anticoagulant effect of warfarin.However, with the increasing number of patients with cardiovascular disease and more and more cases of warfarin combined with statin, it is still necessary to strengthen the monitoring of INR value and bleeding risk when the two drugs are combined.
For the impact of broad-spectrum antibiotics on warfarin PD, some studies confirm that broad-spectrum antibiotics can affect the anticoagulant effect of warfarin 34,35 .Several studies show that chloramphenicol, cefazolins, cefoperazone, cefotaxime, and erythromycin can reduce the absorption of vitamin K. Combination with warfarin can prolong the synthesis time of prothrombin, making warfarin anticoagulant enhanced.Metronidazole, chloramphenicol, etc. can inhibit the CYP enzyme activity in the liver, thereby reducing the clearance rate of warfarin and enhancing its anticoagulant effect.In this study, it shows that the model parameter EC50 of broad-spectrum antibiotics and warfarin has little correlation, which may be because the patients taking roxithromycin and azithromycin have no significant effect on the anticoagulant effect of warfarin, accounting for about 50% of the total patients taking antibiotics.

Evaluation of the predictive performance of each research model
There is a certain correlation between the prediction dose of the five models and the actual clinical dose (P < 0.001), and the models with a strong positive correlation between the prediction dose and the actual dose (r > 0.07) are the Alfalfa-Warfarin-PPK/PD model and the Hamberg model, which are 0.767 and 0.720 respectively, among which the Alfalfa-Warfarin-PPK/PD model has a stronger correlation.The prediction dose and actual dose of the remaining models are moderately correlated (r = 0.04-0.07).In the comparison of the mean prediction error, the model whose MPE value less than the minimum divided dose of warfarin (0.625 mg/day) is the Alfalfa-Warfarin-PPK/PD model and the Hamberg model, indicating that the prediction dose of these two models is close, compared with the actual stable dose of the patient.The prediction dose of the Alfalfa-warfarin-PPK/PD model is closest to the actual dose of warfarin.
In the prediction percentage analysis, the higher prediction percentage the model overestimates, the higher probability of the prediction dose calculated by the selected model is higher than the actual dose, and the greater the risk of bleeding will be in patient taking the prediction dose 36 .The highest ideal prediction percentage in this study is the Alfalfa-Warfarin-PPK/PD model, which is as high as 72.6%, indicating that among these models, the risk of thrombosis and hemorrhage is the lowest using prediction warfarin dose by the Alfalfa-Warfarin-PPK/PD model, followed by the Hamberg model.The percentage of underestimated predictions is low for all models, and the percentage of overestimated predictions is higher except for the Alfalfa-Warfarin-PPK/PD model, indicating that these models are more likely to overpredict patients actual dose and the risk of bleeding in patients dosed as predicted by these models may be higher than the risk of thrombosis.This may be because the distribution frequency of gene polymorphisms in the Chinese population is different from other ethnic groups.The frequency of CYP2C9*3 gene distribution in the sample of this study is only 4.16%.Several studies show that the frequency distribution of CYP2C9*3 gene in the Chinese population is relatively low, which is about 3.5%, and up to 18% in other ethnic groups 37,38 .The frequency distribution of the VKORC1-1639AA genotype in the sample is as high as 92.03%, and related studies show that the distribution frequency of the VKORC1-1639AA genotype in the Asian population is significantly higher than that in the Caucasian population, with a distribution frequency of about 80.4%, but the frequency distribution in the Caucasian population is less than 50% of the total population 39,40 41 .Together with other influencing factors, a prediction model of patient maintenance dose is constructed by multiple linear regression method.Our PK is directly fixed as the parameter estimation value of the literature model, and the EC50 value of the model parameter of PD is based on a wide range of Chinese Han population data, combined with the maximum posterior Bayes method, and re-estimated according to the data characteristics of Chinese Han population.Not only can the initial dose of warfarin be formulated, but the maintenance dose of warfarin can also be predicted "point-to-point" through Bayesian feedback.The shortcomings in this study are as follows: The effects of other concomitant drugs on the pharmacokinetics of warfarin has not been considered, and only the effects of statins, broad-spectrum antimicrobials, azole antifungals, and amiodarone on the pharmacokinetics of warfarin, which have a large number of concomitant patients, has been analyzed.However, in clinical practice, some patients will combine other drugs that may interact with warfarin, such as antihypertensive drugs, hypoglycemic drugs and traditional Chinese medicines, which may affect the pharmacokinetics of warfarin.In the process of data verification in this study, it has not been completely randomized, and when evaluating the efficacy of each warfarin model, no prospective intervention has been carried out.If prospective intervention could be carried out, it could also evaluate the standard time and adverse reactions of patients according to the model prediction of drug administration and routine administration, which can better guide clinical medication.
This study also shows that the R 2 value in the dose model formula is quite different from the prediction accuracy of the model.The studies by Shin et al. also show that the R 2 value during modeling and whether the model has been internally verified are irrelevant with the model's prediction of warfarin dose 42 .Compared with other models, the prediction dose of the Alfalfa-Warfarin-PPK/PD model is the closest to the actual dose (MPA = 0.39 mg/day), and the ideal prediction percentage is the highest (72.56%).It shows that when the prediction dose of this model is used, the probability of bleeding or thrombosis is the lowest when compared with that of other models, and it has better clinical application value.
part of the study is based on the model published by Hamberg, based on extensive data of Han population, combined with the maximum a posterior Bayesian method, to establish a warfarin PPK/PD model suitable for Han population.It can not only predict the initial dose of warfarin like the model constructed by the traditional MAR method, but also can reach the followings: (1) predict the INR value under a given dose maintenance; (2) realize the dose and INR value in an unsteady state, achieve the target INR value as soon as possible, and avoid excessive anticoagulation or insufficient anticoagulation.

Figure 2 .
Figure 2. The correlation between the actual average daily dose of warfarin and the prediction dose of the prediction model (Dots represent: warfarin doses; Solid lines: represent regression curves).
This study is the first time to use the Chinese as a sample to conduct an broader study of warfarin PPK/PD model and INR prediction mode.The PPK model is based on Hamberg's model and uses a wide range of Chinese population data to estimate PPK model parameters applicable to Chinese Han population.Compared with the widely used Hamberg model, Alfalfa-warfarin-PPK/PD model includes two more covariates (body weight and amiodarone), and has better goodness of fit, stronger stability, and better predictive performance.It can achieve dose and the mutual calculation of INR values, and better predict the distribution characteristics of INR values after warfarin administration in the Chinese population.

Table 2 .
Covariate model building process.CM1: whether amiodarone is used in combination; WT: body weight.
Vol.:(0123456789) Scientific Reports | (2024) 14:14846 | https://doi.org/10.1038/s41598-024-65048-7www.nature.com/scientificreports/ Because many hospitals in China use the Gage model and IWPC model for the detection of warfarin VKORC1 and CYP2C9 gene polymorphisms, and guide medication according to the FDA's warfarin dose recommendation table.The previous part of the Alfalfa-Warfarin-PPK/PD model is built on the basis of the Hamberg model.Finally, IWPC dose model, Gage dose model, FDA warfarin application guidance, Hamberg model and Alfalfa-Warfarin-PPK/PD model are selected for the comparison and evaluation of predictive efficacy.Details of the included models can be found in Supplementary Material Table1.
Vol:.(1234567890) Scientific Reports | (2024) 14:14846 | https://doi.org/10.1038/s41598-024-65048-7 . Most of the above models are based on European populations.For example, the FDA warfarin dosage guidelines, Gage model and Hamberg model are all based on European and American populations.Most of the populations in the WICP model are also European and American populations.Compared with other Chinese population models, our study includes patients in a larger number of centers, and is not limited to patients after heart valve replacement.In the study of Zhu et al., a new population pharmacokinetic model is established and individual apparent clearance is obtained